25.2 fraction numbers
In any language there is a mixing between ordinal numbers and fraction numbers, although they have nothing to do with each other. In general, in all languages, the first three numbers have their proper form. Beyond these numbers some languages uses the same form for the fraction and the ordinal numbers. (English is actually very restrictive concerning this issue. In roman languages for the first ten numbers there is no difference between the fraction number and the ordinal number.)
| fraction numbers | ordinal numbers |
| a whole | first |
| a half | second |
| a third | third |
| a quarter | forth |
| a fifth | fifth |
| a sixth | sixth |
| a eighth | eigtht |
| a ninth | ninth |
| a tenth | tenth |
Latin doesn't have fraction numbers and from the very beginning ordinal numbers were used as well as fraction numbers: primus, secundus, tertius, quartus, quintus, sextus, septimus, octavus, nonus, decimus. The only language known by the author that distinguishes completely between fraction numbers and ordinal numbers is german.
However beyond a certain size the ordinal numbers are so complicated, see 25.1. that it is is not possible to express fraction with ordinal numbres. 3/121 would be ~ três / centésimos vigésimos primeiros. Therefore in the course of history a new system was created. Fraction numbers beyond ten can be formed as well by adding -avo, although for some numbers the original ordinal number can still be used, at least in theory.
For the first ten fraction numbers the original latin ordinal numbers are used.meio = halbe  |
| 1/2 = um meio (one half) |
| 3 / 2 = três meios ( three half) |
| terço = drittel |
| 1/3= um terço (one thirdl) |
| 2 / 3 = dois terço (two third) |
| quarto = viertel |
| 1/4 = um quarto (one quarter) |
| 3 / 4 = três quartos ( three quarters) |
| quinto =fünftel |
| 1/5= um quinto (one fifth) |
| 4 / 5 = quatro quintos (four fifth) |
| sexto = sechstel |
| 1/6 = um sexto (one sixth) |
| 3 / 6 = três sextos (three sixth) |
| sétimo = siebtel |
| 1/7 = um sétimo (one seventh) |
| 5 / 7 = cinco sétimos (five seventh) |
| oitavo = achtel |
| 1/8= um oitavo (one eighth) |
| 7 / 8 = nove oitavos (seven eighthl) |
| nono = neuntel |
| 1/9= um nono (one nineth) |
| 8 / 9 = oito / nonos (eight nineth) |
| décimo = zehntel |
| 1/10 = um decimo (one tenth) |
| 4 / 10 = quatro décimos (four tenth) |
For the fraction numbers beyond ten there are sometimes two forms.The tenth, the eleventh, the twelfth and the round fractions (tenth, twentyth, hundredth, four hundredth, thousandts, millionth etc.) have their own forms.
However even these numbers are monsters and difficult to remember because some of them doesn't steem from cardinal numbers and it is therefore to assume that the avo form is preferred.
| fraction numbers | ||
| 10 | décimo | dez avos |
| 11 | undécimo | onze avos |
| 12 | duodécimo | doze avos |
| 13 | - | treze avos |
| 14 | - | quatorze avos |
| 15 | - | quinze avos |
| 16 | - | dezesseis avos |
| 17 | - | dezessete avos |
| 18 | - | dezoito avos |
| 19 | - | dezenove avos |
| 20 | vigésimo | vinte avos |
| 21 | - | vinte e um avos |
| 30 | trigésimo | trinta avos |
| 40 | quadragésimo | quarenta avos |
| 50 | quinquagésimo | cinquenta avos |
| 60 | sexagésimo | sessenta avos |
| 70 | septuagésimo | setenta avos |
| 80 | octogésimo | oitenta avos |
| 90 | nonagésimo | noventa avos |
| 100 | centésimo | cem avos |
| 112 | - | cento e doze avos |
| 200 | ducentésimo | duzentos avos |
| 300 | tricentésimo | trezentos avos |
| 400 | quadringentésimo | quatrocentos avos |
| 500 | quingentésimo | quinhentos avos |
| 600 | sexcentésimo | seiscentos avos |
| 700 | septingentésimo | setecentos avos |
| 800 | octingentésimo | oitocentos avos |
| 900 | nongentésimo | novecentos avos |
| 1.000 | milésimo | mil avos |
| 1.100 | - | mil e cem avos |
| 1.500 | - | mil e quinhentos avos |
| 3597 | - | três mil quinhentos e noventa e sete avos |
| 10.000 | décimo milésimo | dez mil avos |
| 100.000 | centésimo milésimo | cem mil avos |
| 110.000 | - | cento e dez mil avos |
| 1.000.000 | milionésimo | um milhão avos |
(For those who are interested: In Spanish the form with -avos can be used as an ordinal number as well, but not in Portuguese. It is to assume that the Portuguese avoid construction like o ducentésimo quinquagésimo nono homem, the 259th man, by using a glossing-over, someting like o homem numero duzentos cinquenta e um. Concerning the origin of -avo there is a not very convincing theory. It is said that the term steems from ancient egipt, see FRAÇÕES?. Following this theory the ancient egypts had a measure to survey the land but not every land was exactly a multiple of this measure and therefore the used one eighth of this measure, for instance 4 + 2/8 in case that this was needed and eighth is octavus in latin and from this octavus only survived avus and avus becomes avo. The problem is, that the egypts never spoke latin, at most they spoke, after Alexander has conquered the country, greek or macedonian or whatever.)
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